But you are oversimplifying the facts. She is biologically male, but has gender identity disorder. This means that she identifies with being a woman.

male/female != man/woman

This is a fact accepted by the vast majority of psychologists, anthropologists, and sociologists. Denying this fact and refusing to recognize her gender is what makes you seem transphobic. Having reservations about her performing in contact sports with females is reasonable. Refusing to accept her gender identity is not.